Is it possible to elongate particles based on velocity?
Half of the solution (read below) with animation nodes
I got close to the solution using animation nodes. It might be very easy to work on this to make it a complete solution but, I must admit, it's my first time using AN!

I've used Animation Nodes v2.0.
The plane (Plane) emits a particle system with 3 particles with a starting normal velocity and default newtonian physics. Particles must not be displayed via the particle system Render settings. In fact, we'll do it using animation nodes. I've also created a &quot;water drop&quot; mesh (Sphere) for duplication.
This is my animation node setup:

It creates as many copies of Sphere as there are (alive) particles, then it scales them along their Z axis by an amount proportional to each one's Velocity vector length. Finally, it rotates the instances to match the direction of the velocity.
HOWEVER, I am not able to pass a list of rotations to the &quot;Transform Output&quot; node, so I'm only passing ONE rotation, namely that of the first particle!!
If anyone knows how to pass a list of rotations instead of a single rotation, feel free to add a new answer.

Blend file (requires animation nodes):